Certification Problem
Input (TPDB TRS_Standard/Various_04/18)
The rewrite relation of the following TRS is considered.
|
+(*(x,y),*(x,z)) |
→ |
*(x,+(y,z)) |
(1) |
|
+(+(x,y),z) |
→ |
+(x,+(y,z)) |
(2) |
|
+(*(x,y),+(*(x,z),u)) |
→ |
+(*(x,+(y,z)),u) |
(3) |
Property / Task
Prove or disprove termination.Answer / Result
Yes.Proof (by AProVE @ termCOMP 2023)
1 Rule Removal
Using the
Knuth Bendix order with w0 = 1 and the following precedence and weight functions
| prec(u) |
= |
2 |
|
weight(u) |
= |
1 |
|
|
|
| prec(*) |
= |
1 |
|
weight(*) |
= |
0 |
|
|
|
| prec(+) |
= |
0 |
|
weight(+) |
= |
0 |
|
|
|
all of the following rules can be deleted.
|
+(*(x,y),*(x,z)) |
→ |
*(x,+(y,z)) |
(1) |
|
+(+(x,y),z) |
→ |
+(x,+(y,z)) |
(2) |
|
+(*(x,y),+(*(x,z),u)) |
→ |
+(*(x,+(y,z)),u) |
(3) |
1.1 R is empty
There are no rules in the TRS. Hence, it is terminating.